ĐKXĐ: x<>1 và y<>0

\(\left\{{}\begin{matrix}\dfrac{1}{x-1}+\dfrac{1}{y}=-1\\\dfrac{3}{x-1}-\dfrac{2}{y}=7\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{2}{x-1}+\dfrac{2}{y}=-2\\\dfrac{3}{x-1}-\dfrac{2}{y}=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{x-1}=5\\\dfrac{1}{x-1}+\dfrac{1}{y}=-1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x-1=1\\\dfrac{1}{y}=-1-1=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-\dfrac{1}{2}\end{matrix}\right.\left(nhận\right)\)

Nếu 3 số lẻ tiếp biết trung bình cộng = 55 thì:

55 chính là số ở giữa. Vì vậy 3 số lẻ liên tiếp là: 53, 55, 57

A

1 was repaired

2 Was - bought

3 are watered

4 wasn't learned

5 was watched

6 Is - read

7 was stolen

8 was broken

9 wasn't cut

10 is cleaned

was repaired

was-bought

are watered

\(n_{AgNO_3}=1.0,5=0,5\left(mol\right);n_{HCl}=2.0,3=0,6\left(mol\right)\)

PTHH: AgNO₃ + HCl → AgCl ↓ + HNO₃

Mol:      0,5          0,5                          0,5

Ta có: \(\dfrac{0,5}{1}< \dfrac{0,6}{1}\)⇒ AgNO₃ pứ hết, HCl dư

* V_{dd sau pứ} = 0,5+0,6 = 1,1 (l)

\(\Rightarrow C_{M_{ddNO_3}}=\dfrac{0,5}{1,1}=0,4545M\)

\(C_{M_{ddHCldư}}=\dfrac{0,6-0,5}{1,1}=0,0909M\)

\(m_{ddAgNO_3}=500.1,2=600\left(g\right);m_{ddHCl}=300.1,5=450\left(g\right)\)

* m_{dd sau pứ} = 600+450 = 1050 (g)

\(C\%_{ddHNO_3}=\dfrac{0,5.63.100\%}{1050}=3\%\)

\(C\%_{ddHCl}=\dfrac{\left(0,6-0,5\right).36,5.100\%}{1050}=0,348\%\)

D

B

_HT_

B

g: A<1

=>\(\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}< 1\)

=>\(\dfrac{2\sqrt{x}-1-\sqrt{x}-1}{\sqrt{x}+1}< 0\)

=>\(\sqrt{x}-2< 0\)

=>\(\sqrt{x}< 2\)

=>0<=x<4

Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}0< =x< 4\\x< >1\end{matrix}\right.\)

h: \(A=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}\)

=>\(A=\dfrac{2\sqrt{x}+2-3}{\sqrt{x}+1}=2-\dfrac{3}{\sqrt{x}+1}\)

\(\sqrt{x}+1>=1\forall x\) thỏa mãn ĐKXĐ

=>\(\dfrac{3}{\sqrt{x}+1}< =\dfrac{3}{1}=3\forall x\) thỏa mãn ĐKXĐ

=>\(-\dfrac{3}{\sqrt{x}+1}>=-3\forall x\) thỏa mãn ĐKXĐ

=>\(-\dfrac{3}{\sqrt{x}+1}+2>=-3+2=-1\forall x\) thỏa mãn ĐKXĐ

=>\(A>=-1\forall x\) thỏa mãn ĐKXĐ

Vậy: \(A_{min}=-1\) khi x=0

i: \(P=A\left(-x+2\sqrt{x}+3\right)\)

\(=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}\cdot\left(-1\right)\cdot\left(x-2\sqrt{x}-3\right)\)

\(=\dfrac{1-2\sqrt{x}}{\sqrt{x}+1}\cdot\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)

\(=\left(1-2\sqrt{x}\right)\left(\sqrt{x}-3\right)\)

\(=\sqrt{x}-3-2x+6\sqrt{x}=-2x+7\sqrt{x}-3\)

\(=-2\left(x-\dfrac{7}{2}\sqrt{x}+\dfrac{3}{2}\right)\)

\(=-2\left(x-2\cdot\sqrt{x}\cdot\dfrac{7}{4}+\dfrac{49}{16}-\dfrac{1}{16}\right)\)

\(=-2\left(\sqrt{x}-\dfrac{7}{4}\right)^2+\dfrac{1}{8}< =\dfrac{1}{8}\forall x\) thỏa mãn ĐKXĐ

Dấu '=' xảy ra khi \(\sqrt{x}-\dfrac{7}{4}=0\)

=>\(\sqrt{x}=\dfrac{7}{4}\)

=>\(x=\dfrac{49}{16}\)

\(\dfrac{8}{20}\)

1/20 và 8/20

\(\dfrac{8}{20}\)

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